Astute waif initially avoided scrap (5)

I believe the answer is:

shred

'scrap' is the definition.
(both can mean a small amount of material)

I can't explain the remainder of the clue.

(Other definitions for shred that I've seen before include "Torn-off fragment" , "Rip up" , "Bit of cloth" , "Strip of material; a very small amount" , "Tatter; small amount" .)

I've seen this clue in The Times.

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